Question: Factor completely. $5x^4-20x^3+20x^2=$
Solution: As a first step, let's see if there's a common factor we can factor out. Greatest common factor The greatest common factor of $5x^4$, $-20x^3$, and $20x^2$ is $5x^2$. Let's factor $5x^2$ out of $5x^4-20x^3+20x^2$ : $\begin{aligned} &\phantom{=}5x^4-20x^3+20x^2 \\\\ &=5x^2(x^2)+5x^2(-4x)+5x^2(4) \\\\ &=5x^2(x^2-4x+4) \end{aligned}$ We can keep factoring the expression by factoring $x^2-4x+4$. Factoring $x^2-4x+4$ We notice this expression has the perfect square pattern: $\begin{aligned} &\phantom{=}x^2-4x+4 \\\\ &=(x)^2+2(x)(-2)+(-2)^2 \\\\ &=(x-2)^2 \end{aligned}$ [Is there another way to factor this?] Putting it all together $\begin{aligned} &\phantom{=}5x^4-20x^3+20x^2 \\\\ &=5x^2(x^2-4x+4) \\\\ &=5x^2(x-2)^2 \end{aligned}$ In conclusion, this is the completely factored expression: $5x^2(x-2)^2$